Direct reciprocity, stemming from repeated interactions among players, is one of the fundamental mechanisms for understanding the evolution of cooperation. However, canonical strategies for the repeated prisoner's dilemma, such as Win-Stay-Lose-Shift and Tit-for-Tat, fail to consistently dominate alternative strategies during evolution. This complexity intensifies with the introduction of spatial structure or network behind individual interactions, where nodes represent players and edges represent their interactions. Here, we propose a new strategy, ``Cooperate-Stay-Defect-Tolerate" (CSDT), which can dominate other strategies within networked populations by adhering to three essential characteristics. This strategy maintains current behaviour when the opponent cooperates and tolerates defection to a limited extent when the opponent defects. We demonstrate that the limit of tolerance of CSDT can vary with the network structure, evolutionary dynamics, and game payoffs. Furthermore, we find that incorporating the Always Defect strategy (ALLD) can enhance the evolution of CSDT and eliminate strategies that are vulnerable to defection in the population, providing a new interpretation of the role of ALLD in direct reciprocity. Our findings offer a novel perspective on how cooperative strategy evolves on networked populations.
On the existence of fair zero-determinant strategies in the periodic prisoner's dilemma game
Graduate School of Sciences and Technology for Innovation, Yamaguchi University（山口大学创新科学技术研究生院）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理系）
Note: Evolutionary Game Theory Focus Informational Health: The Cocktail Party Effect Through Werewolfgame under Incomplete Information and ESS Search Method Using Expected Gains of Repeated Dilemmas
Graduate School of Sciences and Technology for Innovation, Yamaguchi University（山口大学创新科学技术研究生院）；Department of Mathematical and Systems Engineering, Shizuoka University（静冈大学数学系统工程系）
